Rearrange the Square

Simply cutting a corner off a square can lead to a puzzling activity.

So the little triangle is removed:


This little triangle is then put back making sure that a corner of the triangle is always touching a corner of the shape that the triangle came from, and two edges line up.

We can then make new shapes:


Which were made as follows:



So here's the challenge: Can you make all the following and tell us about how they are made from the two shapes?